Modal Logic

Description

Describe things in terms of possibility and necessity. Also explore how they
intertwine.

For possibility, do not state things in terms of absolute truth, but say how likely
things may be. Use words like seldom, often, probable, possibly, could,
unusual.

For necessity, talk about how necessary something is. Thus use words
like can, may, should, ought, must, have to.

Talking about how true or necessary
something is gives you more potential in arguments as you now have an analog continuity of alternatives,
rather than the black-and-white binary decision of simply whether something is
true or false, necessary or unnecessary.

Example

Say this

Not this

The door might be open.

The door is open.

You must do it.

You do it.

They could come here.

They will come here.

Discussion

Traditional logic is based on extension, in that the truth of the
logic is found within the supporting statements. Modal logic is based on
intention, in that truth is where you find it, and that the reality of many
situations is that it is impossible to determine exact truth.

Thus:

A sentence is possible if it might be true (or might be
false).

A sentence is necessary if it must be true (and cannot
possibly be false).

A sentence is contingent if it is not necessarily true. (a contingent
truth is true in the given case, but might not have been true).

Necessity and possibility have aspects of a Boolean relationship in that:

It is not necessary that X is true = It is
possible that X is not true

It is not possible that X is true = It is necessary that X
is not true

The modalities of possibility and necessity are also known as alethic
modalities.

Deontic logic is the specific logic about duty, where necessity is has
a moral quality to it.